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Something i've been wondering about with gravity and light:

Assuming the speed of gravity is c, does an objects gravitational field have to slow down as light it emits slows down? i.e. as an extreme example, if an object is falling towards a black hole, any light it emits takes longer and longer to reach an observer as it nears the event horizon, so it's gravitational field should take longer and longer [presumably equally as long] to reach the observer as well.

If that is true, can a blackhole's gravitational pull ever increase? Would it be possible to have the object's (delayed) gravitional field exist near the event horizon, and have the blackhole's gravity increase?

Or is it possible that an objects gravitational field can exceed its light cone?

Assuming the speed of gravity is c, does an objects gravitational field have to slow down as light it emits slows down? i.e. as an extreme example, if an object is falling towards a black hole, any light it emits takes longer and longer to reach an observer as it nears the event horizon, so it's gravitational field should take longer and longer [presumably equally as long] to reach the observer as well.

If that is true, can a blackhole's gravitational pull ever increase? Would it be possible to have the object's (delayed) gravitional field exist near the event horizon, and have the blackhole's gravity increase?

Or is it possible that an objects gravitational field can exceed its light cone?

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